Bow and Warp

Therefore, the thickness of a wafer can be deduced. Beyond this, and more importantly, the tool enables the roughness, referencing to the upper and lower probes, to be measured, which can be converted to the so-called flatness, bow, and warp. Flatness, warp, and bow are defined in the following sections. 

The simplest construction for veneered particleboard is a face and back veneer glued to the particleboard core. It is imperative that veneers of equal thickness, grain direction, and dimensional stability be used to insure a balanced panel. A balanced panel reduces the potential for bowing and warp on subsequent exposure to changes in ambient relative humidity. 

The second definition of the purpose of a carrier was to remove the overburden of material above a surface above the device plane. For present purposes, we define the device level as the boundary between the material one wishes to remove and the material one wants to keep. It is not necessarily planar, and it moves up with each layer. For oxide CMP, this layer lies within the topmost film layer. For metal CMP, this surface is defined by the topmost surface of the dielectric into which lines and vias are etched for a damascene process. This definition must accommodate a wafer with a modest amount of bow, tilt, warp, and total thickness variation. Furthermore, it must accommodate very modest amounts of bow, warp, tilt. 

Because of the thermal contraction mismatch of a silicon chip, metal lead-frame and silica-filled epoxy molding compound integrated circuit (IC) packages bow or warp when cooled to room temperature after manufacture. The magnitude of the bow in an IC package can be determined quantitatively by... 

A related issue has to do with the initial wafer-level uniformity (wafer thickness, wafer warp and bow, thicknesses of thin films across the wafer surface, uniformity of stress in such thin films across the wafer) and the subsequent impact on wafer-level polish performance. Some examination has been made of the impact of wafer warp and bow on the polish performance [68], where it was found that the initial warpage can have significant impact (with the implication that reclaimed wafers may not be appropriate monitors of wafer-level polish performance). Other work has considered inherent variation due to Von Mises stress concentrations at the edge of the wafer (conceptually, a downward pressure on the wafer causes lateral stress buildup near the edge of the wafer) [64]. 

Fig. 13. Schematic of a wafer shape measured using a noncontact capacitance probe. The warp and bow are exaggerated. (Courtesy of ADE Corporation, Westwood, MA.)...

I will argue that problem 7 contains not only its own solution but a practical approach to the first six. This solution is apt to be counterintuitive, since it relies on the fact that the curve describing how people discount delayed rewards is warped not only steep, but markedly bowed downwards. Carrying this observation to its logical conclusions may seem unnatural. We do not like to think of our world as being curved people resisted the Greeks deduction that the world was round until Magellan made the conclusion inescapable, and we have... 

Specimen 5 (Fig. 1) was selected for analysis because like specimen 1, it too is an obvious adhesive failure. However, unlike specimen 1, it contained several unique surface features that made it difficult to analyze. Among these were thick adhesive fragments, bondline voids (probably from air bubbles), and shallow (a few fibers) wood failure. Four of the observers declared near complete adhesive failure. However, one observer viewed it veiy differently (85 % wood failure). In this case, the profilometer analysis did not agree well with visual observations. This was due to considerable warp (cup and bow), which severely compromised the analysis. 

This leaves PMMA and PC as the contenders. The disc design is asymmetric, with an impermeable aluminium coating on one side, so dimensional changes caused by water diffusing into the polymer make the disc bow. The water absorption of PMMA at saturation relative humidity is 2.1wt.%, compared with 0.4% for PC. The diffusion constants at 23 °C for water are 0.5 x 10 and 4.8 x 10 mm s , respectively. The CD surface warping must be less than 0.6°, for the laser spot to focus properly. This rules out a PMMA disc with one side sealed, because it would expand over a period of tens of days as water diffuses through the 1mm thick... 

LTCC tapes are offered in multiple thicknesses. In one LTCC material system, fired thicknesses of 1.7, 3.8, 5.5, and 8.5 mil are available. Combinations of any of these thicknesses may be used in a structure however, it is recommended that a symmetrical stackup be used to minimize potential process or mechanical problems such as warp and bow. 

Performance. Desired qualities in a backup material are minimal thickness variations, flatness (no bow, warp, or twist), no abrasives or contaminants, a smooth surface, low cutting energy (minimizing drilling temperatures), and a surface hardness that supports the laminate copper surface (to prevent burrs) yet does not cause damage or extensive wear to the drill bit. 

The market development efforts from 1990 to 1995 for these grades of compounded SPS revolved around applications requiring heat, chemical and electrical properties combined with ease of manufacture, and a unique property of dimensional stability for a semicrystalline plastic material. This last property is due to the fact that the density of the crystalline and the amorphous phases of SPS are almost identical. This has the practical effect that the development of the crystalline phase during cooling does not impart warp or bow in fabricated parts to nearly the extent of most other polymers in this class. 

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